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Mathematics
Problem
Which of the following is the correct expression for
d
d
x
(
a
u
(
x
)
)
\dfrac{d}{dx}\bigl(a^{u(x)}\bigr)
d
x
d
(
a
u
(
x
)
)
, where
a
>
0
,
a
≠
1
a>0,\;a\neq1
a
>
0
,
a
=
1
and
u
(
x
)
u(x)
u
(
x
)
is a differentiable function of
x
x
x
? a)
a
u
(
x
)
u
′
(
x
)
a^{u(x)}\,u'(x)
a
u
(
x
)
u
′
(
x
)
b)
a
u
(
x
)
ln
a
a^{u(x)}\,\ln a
a
u
(
x
)
ln
a
c)
a
u
(
x
)
ln
a
u
′
(
x
)
a^{u(x)}\,\ln a\,u'(x)
a
u
(
x
)
ln
a
u
′
(
x
)
d)
a
u
(
x
)
u
(
x
)
ln
a
a^{u(x)}\,u(x)\,\ln a
a
u
(
x
)
u
(
x
)
ln
a
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